On the Convergence of Adaptive Nonconforming Finite Element Methods for a Class of Convex Variational Problems
On the Convergence of Adaptive Nonconforming Finite Element Methods for a Class of Convex Variational Problems
复制标题
关于一类凸变分问题的自适应非协调有限元方法的收敛性
DOI：
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发表时间：
2011
影响因子：
2.9
通讯作者：
D. Praetorius
中科院分区：
文献类型：
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作者：
C. Ortner;D. Praetorius
建立并分析了一种求解凸变分问题的自适应非协调有限元方法。我们承认的这类极小化问题包括没有欧拉-拉格朗日方程(或不等式)可用的高度奇异问题。因此，我们的论点只使用能量泛函的结构。尽管如此，我们仍然能够证明自适应算法的收敛，即使使用不是可靠的错误指示符的精化指示符。
We formulate and analyze an adaptive nonconforming finite element method for the solution of convex variational problems. The class of minimization problems we admit includes highly singular problems for which no Euler-Lagrange equation (or inequality) is available. As a consequence, our arguments only use the structure of the energy functional. We are nevertheless able to prove convergence of an adaptive algorithm, using even refinement indicators that are not reliable error indicators.